02621nam a2200385 i 4500991003324909707536m o d cr cnu|||unuuu170207s2014 sz a ob 001 0 eng d9783319022727 (pbk.)b1431616x-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.3523AMS 35L45AMS 35L40AMS 35L55Nishitani, Tatsuo59540Hyperbolic systems with analytic coefficients :well-posedness of the Cauchy problem /Tatsuo NishitaniCham :Springer,2014viii, 237 p. :ill. ;24 cmtextrdacontentunmediatedrdamediavolumerdacarrierLecture notes in mathematics,0075-8434 ;2097Includes bibliographical references and indexNecessary conditions for strong hyperbolicity ; Two by two systems with two independent variables ; Systems with nondegenerate characteristicsThis monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearbyCauchy problemDifferential equations, Hyperbolic.b1431616x07-02-1707-02-17991003324909707536LE013 35L NIS12 (2014)12013000293981le013pE44.99-l- 01010.i1579589507-02-17Hyperbolic systems with analytic coefficients820703UNISALENTOle01307-02-17ma -engsz 00